The experimental value of anomalous magnetic moment of muon deviates from its SM prediction at the level of \(4.2\sigma \)  [1]}, [2]}. This difference can be attributed to new physics contributions coming from beyond SM particle(s). In[3]}, a \(U(1)_{L_{\mu }-L_{\tau }}\)  model was considered to explain the muon \((g-2)_{\mu }\)  anomaly. This model also included a DM particle. In this model, the Lagrangian additional to the SM Lagrangian is given as
\(\mathcal {L} = \overline{\chi }i{D}\chi + (D_{\mu }\Phi )^{\dagger }(D^{\mu }\Phi ) - m_{\chi }\overline{\chi }\chi + {\mu }^{2}{\Phi }^{\dagger }\Phi - \lambda ({\Phi }^{\dagger }\Phi )^{2}\,,\) 
